By Web Application I mean a web site targeted at Safari on the iPhone that can run \"off-line\" (by using a cache manifest file, JavaScript database, running full screen fro
Try PhoneGap, also checkout the Building iPhone Apps with HTML, CSS, and JavaScript book.
Is it possible to distribute an iPhone Web Application through the App Store?
To my knowledge, no it is not. Theoretically, you could use a UIWebView to allow the user to experience your iphone-webapp, but if you're a serious developer, the $1000 for a used MacBook and the $100 for an iPhone License are well worth it.
From a different perspective, the iPhone does allow custom links to your website by "Add To Homescreen". This gives the user nearly the same experience as with a native app.
From another perspective, you can achieve offline capability in a similar way to what Google does for Gmail/Reader/etc with its client-side cache/HTML 5.0 stuff.
MonoTouch - This technology has been getting tossed around SO recently, so you might want to check it out (non-OSX developement).
No only native apps can be deployed through the AppStore, I would look into the later option though. i.e. Develop a native app that provided a webkit surface. I think the trickiest bit would be exposing lower level iPhone functionality to the javascript engine.